Properties

Label 3.13
Level 3
Weight 13
Dimension 3
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 8
Trace bound 0

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 13 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(8\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{13}(\Gamma_1(3))\).

Total New Old
Modular forms 5 5 0
Cusp forms 3 3 0
Eisenstein series 2 2 0

Trace form

\( 3 q - 621 q^{3} - 4560 q^{4} + 50544 q^{6} - 73002 q^{7} + 1291059 q^{9} + O(q^{10}) \) \( 3 q - 621 q^{3} - 4560 q^{4} + 50544 q^{6} - 73002 q^{7} + 1291059 q^{9} - 3875040 q^{10} + 8828784 q^{12} - 6829482 q^{13} + 11625120 q^{15} - 14769024 q^{16} - 68234400 q^{18} + 124574118 q^{19} - 166240458 q^{21} + 213127200 q^{22} - 11726208 q^{24} - 158837325 q^{25} + 79381539 q^{27} - 977148192 q^{28} + 2615652000 q^{30} - 397135434 q^{31} - 639381600 q^{33} - 2724928128 q^{34} - 1110844368 q^{36} + 7283710518 q^{37} - 8584304778 q^{39} + 899009280 q^{40} + 2034396000 q^{42} + 17718547398 q^{43} - 15693912000 q^{45} - 19727053632 q^{46} + 33524302464 q^{48} - 14720872599 q^{49} + 8174784384 q^{51} - 49607232672 q^{52} + 65255286096 q^{54} + 49019256000 q^{55} - 58974235002 q^{57} - 22071722400 q^{58} - 50313519360 q^{60} - 7295998314 q^{61} - 51002631882 q^{63} + 221261786112 q^{64} - 143860860000 q^{66} + 91322348838 q^{67} + 59181160896 q^{69} - 155970360000 q^{70} + 15830380800 q^{72} - 17452607322 q^{73} + 449988631875 q^{75} - 388477014816 q^{76} + 64901023200 q^{78} - 948954743562 q^{79} + 294589969443 q^{81} + 1507375396800 q^{82} - 223181815968 q^{84} - 626733469440 q^{85} + 66215167200 q^{87} - 49445510400 q^{88} - 1471775067360 q^{90} + 1545913657164 q^{91} - 476317306602 q^{93} + 197685401472 q^{94} - 845267125248 q^{96} - 355122301242 q^{97} + 863165160000 q^{99} + O(q^{100}) \)

Decomposition of \(S_{13}^{\mathrm{new}}(\Gamma_1(3))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
3.13.b \(\chi_{3}(2, \cdot)\) 3.13.b.a 1 1
3.13.b.b 2